Which has more atoms: 1 kg of iron oruiq // +pi0zqy 1 kg of aluminum? See the periodic table or y+ izqu0/iqp/ Appendix B.

Name several properti s(5q)0 2rgc. l1ag. bhmuryxb5fr 2fwes of materials that could be exploited to make a thermometer.5(r1fcgrhsyua 22 q b5g.0 )rwlmx bf.

Which is larger, 1 Ck,qm,;s 0yxhy ic5y0 s $^{\circ} $ or 1 F $^{\circ} $?

If system A is in thermal equilibrium with system B, but jri)fchj5qyifyto 8 *4qi9f 97 gzh42B is not in thermal equilibrijzif g*4i 9hirhf 7fct2q8yoy)59q4jum with system C, what can you say about the temperatures of A, B, and C?

A flat bimetallic strip consists of aluminum riveted to a strip of iron. When hebkgp bpw)x.54j9zog, ated, the strip will bend. Which metal will be on the outside of the curve? [Hint: gbpg,wxo b 9k5j4).z pSee Table 13–1.] Why?

In the relation $\Delta$L = $\alpha$ $L_0$ $\Delta$T, should $L_0$ be the initial length, the final length, or does it matter? Explain.

The units for the coefh))( g bvv/.fk )9iz seqfb3gmficient of linear expansion $\alpha$ are $(C?)^{-1}$ and there is no mention of a length unit such as meters. Would the expansion coefficient change if we used feet or millimeters instead of meters? Explain.

Figure 13–27 shows a diagram of a simple thermostat used to co 1 )cs0gw+fqqzntrol a furnace (or other heating or cooling system). The bimetallic strip consists of two strips of different metals bonded together. The electric switch is a glass vessel containing liquid mercury thatzc q)q0 sfgw1+ conducts electricity when it can flow to touch both contact wires. Explain how this device controls the furnace and how it can be set at different temperatures.

Long steam pipes that are fixed at the ends often have a section in the sha)u3x;:qnr9 1kz0bozqtjfi :c( anu -lpe of a f1b ):xqk jnn; cz0(ziruuqao9-tl:3 U. Why?

A flat, uniform cylinder of lead floats in mercury ;x3(/snq ms fym-c/kb at 0 $^{\circ} $ C. Will the lead float higher or lower when the temperature is raised? Explain.

When a cold mercury-in-glass thermometer is first placed iz81flwc8--h) vospuq n a hot tub of water, the mercury inipv8wh 1ofz)8-qu-l sctially descends a bit and then rises. Explain.

A glass container may break if one part of it is heatey a456/furh n loyl)(fd or cooled more rapidly than adjacent parts. Exaln(of6y r4 l)fuh/5y plain.

The principal virtue of Pyrex glass is that its coeffica631esknipcbwg6 2c2pa) 7a *w 5 firmient of linear expansion is much smaller than that for ordinary glass (Table 13–1). Explain why this gives rise to the increased heat resistance of 7npa1 m6a csbp6e25wi2iaf*wgc kr)3 Pyrex.

Will a grandfather clcqo*.)cd4qb g 8x pl6zock, accurate at 20 $^{\circ} $ C, run fast or slow on a hot day (30 $^{\circ} $ C)? Explain. The clock uses a pendulum supported on a long, thin brass rod.

Freezing a can of soda will cause its bottom and top to bulge so badly thpdk8+stbg 1r+ qb0ya(e can will not stand up. Wpra k (by+qg0t1b+sd 8hat has happened?

When a gas is rapidly compressed (say,- ;6jhib/ vyid by pushing down a piston), its temperature increases. When a gas expands against a piston, it cools. Explain these changeiyb d6/h jiv;-s in temperature using the kinetic theory, in particular noting what happens to the momentum of molecules when they strike the moving piston.

Will the buoyant force on an aluminum sphere submerged in water increase or decr-v fm c6w55.4hnkvj* *bogf pgease if the temperature is increased from 20 b-j6*nwof p4c mgf v.5*g5khv $^{\circ} $ C to 40 $^{\circ} $ C?

Explain in words how Charles’s l fd 2cklz)ji1q 4rm5b-aw follows from kinetic theory and the relation between average kinetic energy and the absolute temperature.bilf5z2k1)djc-q m4r

Explain in words how Gay-Lussac’s law fou vc kv9.*etr7llows from kinetic theory.

As you go higher in the Earth’s atmosphere, thexs8 neeryj3 )va41.ekis ;z(o ratio of $N_2$ molecules to $O_2$ molecules increases. Why?

Escape velocity for the Earth refers to the minimum speed an object 5h2+0io ;avsd4o(exwv ow ) fsmust have to a+h 40e25vo xo dwwvi;ssf o)(leave the Earth and never return. The escape velocity for the Moon is about one-fifth what it is for the Earth due to the Moon’s smaller mass. Explain why the Moon has practically no atmosphere.

Alcohol evaporates more quickly than wate0 coki:x.q +aup)j 1pbr at room temperature. What can you infer about the molecular properties of one relati1 x pbqk:)uaoc.ip+ 0jve to the other?

Explain why a hot humid day is faxri :sn 1ei,(sr more uncomfortable than a hot dry day at the same t ,nssx1ir:(i eemperature.

Is it possible to boil water at room temperature (2r j8 s8 yqkbec) ee,e8ggg7g*60 $^{\circ} $ C) without heating it? Explain.

Consider two days whe nomdacj(u2.q (dcd5dy +tdp9e a8 9e3n the air temperature is the same but the humidity is different. Which is more dense, the dry air or the humid8d3ddc.tye d9+an m25 u p9a( qcode(j air at the same T? Explain.

Explain why it is dangerous to open the radiator cap of an over-hiy*sm;qghzt57 :6yxf*yzf t1 zds/heated automobile e- qyfs/zmxt;6:s5gdif ytz1z * hhy7 *ngine.

Why does exhaled air appearey8gj ht r7-l+ as a little white cloud in the winter (Fig. 13–28)?

  How many atoms are there in a 3. 26lgsm7)o9)mi wd: am(hhgnk4-gram copper penny?   $ \times10^{22}$ atoms of Cu

  How does the number of atoms in a 26.5-gram goo 5 ,9twh9,3gjo bpssrld ring compare to the number in a silverp3,jr 9 s5gowhtb9o,s ring of the same mass?$N_{Au}$ =    $N_{Ag}$

  “Room temperature” is often taken to be 68°F. What is 4v9mg aq,by4f this on the Celsius scale?gb9 4qmyv,4af   $^{\circ} $ C
(b) The temperature of the filament in a lightbulb is about 1800 $^{\circ} $ C. What is this on the Fahrenheit scale?    $^{\circ} $ F

  Among the highest and lowest temperatures recorded are 136 cnky(2 )0nnz8kv.. qm 0wk mlx$^{\circ} $F in the Libyan desert and -129 $^{\circ} $F in Antarctica. What are these temperatures on the Celsius scale?high =    $^{\circ} $ C
low =    $^{\circ} $ C

  (a) 15 $^{\circ} $ below zero on the Celsius scale is what Fahrenheit temperature?    $^{\circ} $ F
(b) 15 $^{\circ} $ below zero on the Fahrenheit scale is what Celsius temperature?   $^{\circ} $ C

  In an alcohol-in-glass thermometer, the alcoht39 zcy*jwgkwnl/0b oh4 /cr1ol column has length 11.82 cm at 0.0wy/*lzw1/g0hktjb c rn 3 9o4c $^{\circ} $ C and length 22.85 cm at 100.0 $^{\circ} $ C. What is the temperature if the column has length
(a) 16.70 cm,    $^{\circ} $ C
(b) 20.50 cm?    $^{\circ} $ C

  A concrete highway is built of slabs 12 m long (jt4. s+uwp )vj 4hyd7m6 s;ibt20 $^{\circ} $ C). How wide should the expansion cracks between the slabs be (at 20 $^{\circ} $ C) to prevent buckling if the range of temperature is -30 $^{\circ} $ C to +50 $^{\circ} $ C?    m

  Super Inva$^{TM}$, an alloy of iron and nickel, is a strong material with a very low coefficient of linear expansion [0.2$ \times10^{ -6}$(C?)$^{-1}$]
A 2.0-m-long tabletop made of this alloy is used for sensitive laser measurements where extremely high tolerances are required. How much will this table expand along its length if the temperature increases 5.0 $^{\circ} $ C? Compare to tabletops made of steel.   $ \times10^{-6 }$ m    $ \times10^{-4 }$ m

  The Eiffel Tower (Fig. 13–29) is built of wrought iron approxtzq/ lyix* wly;e8vk1cs 30p:imately 300 m tall. Estimatcyl8 /y : lq;vxt10psz*ek3i we how much its height changes between July (average temperature of 25°C) and January (average temperature of 2 $^{\circ} $ C). Ignore the angles of the iron beams, and treat the tower as a vertical beam.    m

  To make a secure fit, rivets that are larger than the rivet hole are o-lr :8dww- ;1ckkd ikbften used and the rivet is cooled (usually in dry ice) before it is placed in the hole dk1-8 k lk-bc:wdrwi;. A steel rivet 1.871 cm in diameter is to be placed in a hole 1.869 cm in diameter at 20 $^{\circ} $ C. To what temperature must the rivet be cooled if it is to fit in the hole?    $^{\circ} $ C

  The density of water03qrj1f s4u uu at 4 $^{\circ} $ C is $ 1\times10^{3 }kg/m^3$ What is water’s density at 94 $^{\circ} $ C?    kg/$m^3$

  A quartz sphere is 8.75 cm in diamby-8k fluh;0sc(c8yqr: rs: f eter. What will be its change in volume if it is heated frfyq-:yhl(8csc;r8fubk 0s r: om 30 $^{\circ} $ C to 200 $^{\circ} $ C?    $ \times10^{ -2}cm^3$

  An ordinary glass is filled to the brim with 350.0 mL of wate7dh 6l5jj qa otl.nb2ll(qf;7r at 100.0$^{\circ} $ C. If the temperature decreased to 20.0 $^{\circ} $ C, how much water could be added to the glass?    mL

  It is observed that 55.50e /dvu1d(.xd(notv jk6 *l uh5 mL of water at 20 $^{\circ} $ C completely fills a container to the brim. When the container and the water are heated to 60 $^{\circ} $ C, 0.35 g of water is lost. (a) What is the coefficient of volume expansion of the container?    $ \times10^{-5 }$ /$C^0$(b) What is the most likely material of the container? The density of water at 60°C is 0.98324g/ml.

  (a) A brass plug is tsg 47vl zi3djtdyt02 p acm.+-o be placed in a ring made of iron. At 20 $^{\circ} $ C, the diameter of the plug is 8.753 cm and that of the inside of the ring is 8.743 cm. They must both be brought to what common temperature in order to fit?    $^{\circ} $ C
(b) What if the plug were iron and the ring brass?    $^{\circ} $ C

If a fluid is contained in a long, narrow vessel so it cytuwvk 6oo8kcyu2*4 * an expand in essentially one direction only, show that the effective coefficient of linear expansion is approximately equal to the coeff otck wvo*yy84u*6 2ukicient of volume expansion $\beta$.

(a) Show that the change in the densiteqr /6 h 1t.dg4tbg/eyy $\rho$ of a substance, when the temperature changes by $\Delta$T is given by $\rho$ = -$\beta$$\rho$$\Delta$T
(b) What is the fractional change in density of a lead sphere whose temperature decreases from 25 $^{\circ} $ C to -40 $^{\circ} $ C？

A uniform rectangular plate of length l and width w-ac bzfbi))aj2s s*/v g51hwc has coefficient of linear expaascw* c )fgb-zhbjs )a1/i5 v2nsion $\alpha$ Show that, if we neglect very small quantities, the change in area of the plate due to a temperature change $\Delta$T is $\Delta$A = 2$\alpha l w$$\Delta$T See Fig. 13–30.

Show that for an isotropic sol.(7x bov(ezff+looy 4 mi3)icid, $\beta$ = 3$\alpha$ if the amount of expansion is small. $\beta$ and $\alpha$ are the coefficients of volume and linear expansion, respectively. [Hint: Consider a cubical solid, and neglect very small quantities. See also Problem 18 and Fig. 13–30.]

  The pendulum in a grandfatheme ce ye-:no03 xo17jxr clock is made of brass and keeps perfect time at 10o 1 3 cexye-:exjo7mn7 $^{\circ} $ C. How much time is gained or lost in a year if the clock is kept at 25 $^{\circ} $ C? (Assume the frequency dependence on length for a simple pendulum applies.)$\approx$    min(Round to the nearest integer)

  (a) The tube of a mercury thermometer has an inw)gujhk lsm b* ;,hj26side diameter of 0.140 mm. The bulb has au,mkl) *wjhh;jb6gs 2 volume of 0.255 $cm^3$ How far will the thread of mercury move when the temperature changes from 11.5 $^{\circ} $ C to 33.0 $^{\circ} $ C? Take into account expansion of the Pyrex glass.    cm(b) Determine a formula for the length of the mercury column in terms of relevant variables. Ignore tube volume compared to bulb volume.

  A 23.4-kg solid aluminum cylindrical wheel oohtq: d/q5;yjf radius 0.41 m is rotating about its axle on frictionless bearings with an;qdq/hj y5 ot:gular velocity $\omega$ = 32.8 rad/s If its temperature is now raised from 20.0 $^{\circ} $ C to 75.0 $^{\circ} $ C, what is the fractional change in $\omega$?   

  An aluminum bar has the desired length when atrzwpk ( imb)2i(g1 t;hr52eyryvv .0z 15°C. How much stress is required to keep it at this lengtr2by0yt (h w2ipzrkvgr i ;ev(5 1.)zmh if the temperature increases to 35 $^{\circ} $ C?    $ \times10^{7 }$ N/$m^2$

(a) A horizontal steel I-beam of cross-sectional a-x3 ewzoi8cram 0vg*/d3cj 2nrea 0.041$m^2$ is rigidly connected to two vertical steel girders. If the beam was installed when the temperature was 30$^{\circ} $ C, what stress is developed in the beam when the temperature drops to -30 $^{\circ} $ C (b) Is the ultimate strength of the steel exceeded? (c) What stress is developed if the beam is concrete and has a cross-sectional area of 0.13$m^2$ Will it fracture?

  A barrel of diameter 134.129pmnvji ;vg 0/2 cm at 20$^{\circ} $ C is to be enclosed by an iron band. The circular band has an inside diameter of 134.110 cm at 20$^{\circ} $ C. It is 7.4 cm wide and 0.65 cm thick.
(a) To what temperature must the band be heated so that it will fit over the barrel? $\approx$   $^{\circ} $ C(Round to the nearest integer)
(b) What will be the tension in the band when it cools to 20$^{\circ} $ C?    N

  What are the following temperaturef. y9kyjz,gmqhbh g-q7 vo2-+s on the Kelvin scale:
(a) 86$^{\circ} $ C,    K
(b) 78$^{\circ} $F,    K
(c) -100$^{\circ} $C    K
(d) 5500°C,    K
(e) -459$^{\circ} $F    K

  Absolute zero is what temperatur2v rlss/6 .1vn8emj, hbmmj4re on the Fahrenheit scale?    $^{\circ} $ F

  Typical temperatures in the interior of the Ea81ok9 i.7j odw* h9yqhdv*wvy rth and Sun are about 4000$^{\circ} $ C and $ \times10^{6 }$ $^{\circ} $ C respectively.
(a) What are these temperatures in kelvins?    K    $ \times10^{ 6}$K
(b) What percent error is made in each case if a person forgets to change $^{\circ} $ C to K? $\approx$    %(Round to the nearest integer) $\approx$    %(Round to three decimal places)

  If 3 $m^2$ of a gas initially at STP is placed under a pressure of 3.20 atm, the temperature of the gas rises to 38.0$^{\circ} $ C. What is the volume?    $m^3$

  In an internal combustion engine, air at atmospheric pressure and * o5ytl7 tja-+y-hop ya temperature oh 5olja tt +-yy-yo7*pf about 20$^{\circ} $C is compressed in the cylinder by a piston to $\frac{1}{9}$ of its original volume (compression ratio = 9.0). Estimate the temperature of the compressed air, assuming the pressure reaches 40 atm.    $^{\circ} $ C

  Calculate the density of p1yry(dlw -+pstyat:fpm ,1( oxygen at STP using the ideal gas law.    kg/$m^3$

  A storage tank contains 2.;nr+cjq4ipt:d qeb31.6 kg of nitrogen ($N_2$) at an absolute pressure of 3.65 atm. What will the pressure be if the nitrogen is replaced by an equal mass of $CO_2$    atm

  A storage tank at STP contains 18.56;a7f m-zzcvj kg of nitrogen ($N_2$)
(a) What is the volume of the tank? $\approx$   $m^3$(“Round to one decimal places)
(b) What is the pressure if an additional 15.0 kg of nitrogen is added without changing the temperature?    $ \times10^{5 }$Pa    atm

  If 18.75 mol of helium a-q f u)7f:mckgas is at 10.0$^{\circ} $C and a gauge pressure of 0.350 atm, (a) calculate the volume of the helium gas under these conditions.    $m^3$
(b) Calculate the temperature if the gas is compressed to precisely half the volume at a gauge pressure of 1.00 atm.    $^{\circ} $ C

  What is the pressure inside a 35.0-L container holding 105./ru-nxlvi ws(: c5ue.0 kg of argon gas at 3.5u :ewir- /nvlcs(xu85 K?   $ \times10^{ 8}$Pa

  A tank contains 26.0 kg o d5og7 qmqs 4/hnaao .jdg (zs3*/pm4xf $O_2$ gas at a gauge pressure of 8.70 atm. If the oxygen is replaced by helium, how many kilograms of the latter will be needed to produce a gauge pressure of 7.00 atm?    kg He

  A hot-air balloon achieves its buo-fn) e3a0bz1e liz71u fo 4rluyant lift by heating the air inside the balloon, which makes it less dense than the air outside. Suppose the volume of a balloon n4a1ue flz) lfr-07eiz31bu ois 1800 $m^3$ and the required lift is 2700 N (rough estimate of the weight of the equipment and passenger). Calculate the temperature of the air inside the balloon which will produce the required lift. Assume that the outside air temperature is 0 $^{\circ} $ C and that air is an ideal gas under these conditions. What factors limit the maximum altitude attainable by this method for a given load? (Neglect variables like wind.) $\approx$    $^{\circ} $ C(Round to the nearest integer)

  A tire is filled withv27 yv,*z3 be)bx(4aapvi zxe air at 15 $^{\circ} $ C to a gauge pressure of 220 kPa. If the tire reaches a temperature of 38 $^{\circ} $ C, what fraction of the original air must be removed if the original pressure of 220 kPa is to be maintained?    %

  If 61.5 L of oxygen at 18.ek lwka4z+, k-0 $^{\circ} $ C and an absolute pressure of 2.45 atm are compressed to 48.8 L and at the same time the temperature is raised to 50.0°C, what will the new pressure be?    atm

  A helium-filled balloon es5 :htc4l 6tk 5 ubaugjlbm1ic4vg e)17capes a child’s hand at sea level and 20.0 $^{\circ} $ C. When it reaches an altitude of 3000 m, where the temperature is 5.0 $^{\circ} $ C and the pressure is only 0.70 atm, how will its volume compare to that at sea level?    times the original volume

  Calculate the number of molecules / qlvy ie 1e 2s20t0prtb).o5st1pthf;$m^3$ in an ideal gas at STP.    $ \times10^{25 }$ molecules /$m^3$

  How many moles of water are there in 1.000 L? H bum6 r0s11novi)x/vc ow many molecules?    mol    $ \times10^{25 }$ molecules

  Estimate the number of (a) r*w hd(3sn+ya vy(b,cfn / z dtkg95h8moles,    $ \times10^{22 }$ moles and (b) molecules of water in all the Earth’s oceans. Assume water covers 75% of the Earth to an average depth of 3 km. $\approx$    $ \times10^{46 }$ molecules

  A cubic box of volume 5.1cah o i,7ta5z/h. /omn$ \times10^{ -2}m^3$ is filled with air at atmospheric pressure at 20 $^{\circ} $ C. The box is closed and heated to 180 $^{\circ} $ C. What is the net force on each side of the box?    N

  Estimate how many molecules of air are in ea w:smy14h,bhcz- 8np sch 2.0-L breath you inhale that were also in the last breath Galileo took. [Hint: Assume the atmospherz wb1hsms:c,4 8np-hy e is about 10 km high and of constant density.]   $\frac{molecules}{breath}$

  (a) What is the average translational kinetic energy of an oxygen bwk p) nnl+5qi+l:,yr molecule at STPb,inl+rwk5ly+ p:q n )?    $ \times10^{-21 }$ J
(b) What is the total translational kinetic energy of 2.0 mol of $O_2$ molecules at 20 $^{\circ} $ C?   $ \times10^{3 }$ J

  Calculate the rms speed of h /dq3z0vt-lbn wqg(r2elium atoms near the surface of the Sun at a temperature vtnq(rld 02-gzqbw/3of about 6000 K.    m/s

  By what factor will the rms speed of gas molecules ia0vm q ;-gl(flncrease if the temperature is increml ;lf(0 aqg-vased from 0 $^{\circ} $ C to 100 $^{\circ} $ C?   

  A gas is at 20 $^{\circ} $ C. To what temperature must it be raised to double the rms speed of its molecules?    $^{\circ} $ C

  Twelve molecules have the following speeds, given in units of+8jirx;alxif4: 5 qdwb -0rni km/s: 6, 2, 4, 6, 0, 4, 1, 8, 5, 3, dixax- j0lf;5in i:4 r 8+qrwb7, and 8. Calculate the rms speed. $v_{rms}$ =    km/s

  The rms speed of molecules in vn(x tg0jf1ai2ge 1.u a gas at 20.0 $^{\circ} $ C is to be increased by 1.0%. To what temperature must it be raised?    $^{\circ} $ C

  If the pressure of a gas is doubled while its vkvu)b.a a,+jf olume is held constant, by what factor bu ,ajf+)va k.does $v_{rms}$ change?   

Show that the rms speed of molecules inylmgung -9(80p km 2.kv jlou+ a gas is given by $v_{rms}$ = $\sqrt{3P\\rho}$ where P is the pressure in the gas, and $\rho$ is the gas density.

Show that for a mixture of two gases at the same-lf-* 74l luhuej4m6 ; iqzmbq temperature, the ratio of their rms speeds is equal t4m mi;e*bulf67lq u-z4hq l-jo the inverse ratio of the square roots of their molecular masses.

  What is the rms speed of nitrogen mo slnkep4-ww;;m tsg (-lecules contained in an 8.5$-m^3$ volume at 2.1 atm if the total amount of nitrogen is 1300 mol?    m/s

  Calculate (a) the rms speed of an oxygen molecule ;fsa++wpa 0,a*li d s0xwwzo8 at 0 $^{\circ} $ C    m/s
(b) determine how many times per second it would move back and forth across a 7.0-m-long room on the average, assuming it made very few collisions with other molecules.    round trips per sec

  What is the average distanb) f6ccmp7 ugio eo.:;ce between nitrogen molecules at STP?    $ \times10^{-9 }$m

  (a) Estimate the rms speed of an amizp ojzd2.b rk :9:cg4tno acid whose molecular mass is 89 u in a living cellz 9d.r4j:pg:b c tzk2o at 37 $^{\circ} $ C.    m/s
(b) What would be the rms speed of a protein of molecular mass 50,000 u at 37 $^{\circ} $ C?    m/s

Show that the pressure P of a gas can be writtv0rm jwhm mrf ck4)y da3:8:8nen P = $\frac(1)(3)\rho v^2$ where $\rho$ is the density of the gas and v is the rms speed of the molecules.

  The two isotopes of uranium0h; j-b3 sj 4jmdv:evo, $^{235}$U and $^{238}$U (the superscripts refer to their atomic mass), can be separated by a gas-diffusion process by combining them with fluorine to make the gaseous compound UF$_6$ Calculate the ratio of the rms speeds of these molecules for the two isotopes, at constant T.   

(a) At atmospheric pressure, in what phasesjdbit cc41+;isngx 0 9 can $CO_2$ exist? (b) For what range of pressures and temperatures can $CO_2$ be a liquid? Refer to Fig. 13–21.

Water is in which phase when the pressure is 0.01 atm and the temperature is(bq2 2g 6 nvzhanr.uh)aksalj387h 5d (a)a5rnsan khh2vbz 8u .d36lj( hga72)q 90 $^{\circ} $ C, (b) -20 $^{\circ} $ C.

  What is the dew point (approximately) if the humidity is 50% on a da/2;c0u-ryj f4 ja( acw tsmb+uy when the temperatsr ( t20cbu c+awj-;y/uaf4mj ure is 25 $^{\circ} $ C?$\approx$    $^{\circ} $ C(Round to the nearest integer)

  What is the air pressure at a place where aq0 -mqiw3sdqv4 tj( oz1o50uwater boils at 90 $^{\circ} $ C?    torr    Pa    atm

  If the air pressure at a particular place in the moqm9q yn-xcq0) -s-xkmuntains is 0.72 atm, estimate the temperature at which water boils.m ck-)9xx-m0qn-sq yq $\approx$ =    $^{\circ} $ C

  What is the temperature on a day when the partial pressure of water is 530 Pa anwv e+9amix 99m 1gnae0rgqt+) d the relative humidity is 40%a n) et qe9i9mxgv1+g09a+ rwm? $\approx$ =    $^{\circ} $ C(Round to the nearest integer)

  What is the partial pressure of water on a day wheh wa4*vw :pik h)wja5-r;q:jz n the temperature is 25 $^{\circ} $ C and the relative humidity is 35%?    Pa

  What is the approximate pref(9qcrl-e8gpbm. r+)c + aoy.f /oy cussure inside a pressure cooker if the water is boiling at a temperature of 1fr.fcp(uy oyeg-q.l)rb9c8 +o/ +cm a20 $^{\circ} $ C? Assume no air escaped during the heating process, which started at 20 $^{\circ} $ C.    atm

  If the humidity in a ry; ctd 8,ajep+oom of volume 680$m^3$ at 25 $^{\circ} $ C is 80%, what mass of water can still evaporate from an open pan?    kg

  Air that is at its dew poivf t;;,q6cfvwnt of 5 $^{\circ} $ C is drawn into a building where it is heated to 25. What will be the relative humidity at this temperature? Assume constant pressure of 1.0 atm. Take into account the expansion of the air.    %

  Estimate the time needed for a glycine molecule (see Table 13–4) t16/p;7a gfrli:xmvoi1v f:fr o diffuse a distance of gm ::v fv1ax/lpr;if17 roi6f 15 $\mu m$ in water at 20$^{\circ} $ C if its concentration varies over that distance from 1 mol/$m^3$ to 0.4 mol/$m^3$ Compare this “speed” to its rms (thermal) speed. The molecular mass of glycine is about 75 u. t $\approx$    s ([color=rgba(0, 0, 0, 0.85)]Round to one decimal places) $v_{diffuse}$    $ \times10^{ -5}$ m/s
$v_{rms}$    m/s

  Oxygen diffuses from the surface of insects to the interior through tiny tube/dn79xw9rheo4pf qa 6s called tracheae. An9 pf4reh7x9qd onw /6a average trachea is about 2 mm long and has cross-sectional area of $ 2\times10^{-9 } m^2$ Assuming the concentration of oxygen inside is half what it is outside in the atmosphere,
(a) show that the concentration of oxygen in the air (assume 21% is oxygen) at 20$^{\circ} $ C is about 8.7 mol/$m^3$ then $\approx$    mol/$m^3$(Round to one decimal places)
(b) calculate the diffusion rate J,    $ \times10^{-11 }$ mol/s
(c) estimate the average time for a molecule to diffuse in. Assume the diffusion constant is $ 1\times10^{-5 } m^2/s$    s

  A precise steel tape measure z pfnz10e 5qq. gbv9+fhas been calibrated at 20$^{\circ} $C. At 34$^{\circ} $C,
(a) will it read high or low,
(b) what will be the percentage error?    $ \times10^{-4 }$ %

  A precise steel tape mpf6z 1 kco)we 15e/lcyw0zxo3easure has been calibrated at 20$^{\circ} $C. At 34$^{\circ} $C,
(a) will it read high or low,
(b) what will be the percentage error?    $ \times10^{-4 }$ %

  A Pyrex measuring cup was calibrated at normalrb 3svtvh4b3w326ri8o u(kyz4 on x d6 room temperature. How much error will be made in a recipe calling for 300 mL of cool wato(rt4kbu vis rob2y33d wvx48 h3n6z 6er, if the water and the cup are hot, at 80$^{\circ} $C, instead of at 20$^{\circ} $C? Neglect the glass expansion.$\approx$    ml

  The gauge pressure in a hd7:i5kv:zodgb0iz 9wh *t eg( elium gas cylinder is initially 28 atm. After many balloons have been blown up, the gauge pressure has decreased to 5 atm. What fractvogg iz9: w5b dk0dit7z(h:e*ion of the original gas remains in the cylinder?   

  Estimate the number of air molecules in a room of length;pujf3e +ht4l u h*ra:z7rf0o 6.5 m, width 3.1 m, and height 2.5 m. Asr f*;o 3 tu4 70re:ahzlhfjp+usume the temperature is 22$^{\circ} $C. How many moles does that correspond to?    $\times10^{27 }$ molecules    moles

  In outer space the density of ma.vkqrt z xq/r :j(hi7.tter is about one atom per $cm^3$ mainly hydrogen atoms, and the temperature is about 2.7 K. Calculate the rms speed of these hydrogen atoms, and the pressure (in atmospheres).$v_{rms}$ =    m/s    $ \times10^{-22 }$ atm

  The lowest pressure attainable using the best r go*c,mu( h-yavailable vacuum techniques is about ug(ym*hc-,or $10^{-12} N/m^2$ At such a pressure, how many molecules are there per $cm^3$ at 0$^{\circ} $C?    $\frac{molecules}{cm^3}$

  If a scuba diver fills his lungk;+:tz/loi yr s to full capacity of 5.5 L when 10 m below the surface, to what volume would his lungs expand if he quickly rose to the surface? Is +i:t; lr/zykothis advisable?    L

  A space vehicle returning from the Moon enters Earth’s atm np 3:fkct+rm5osphere at a speed of about 40,000 km/h Molecules (assume nitrogen) striking the nose of the vehicle with this speed correspond to wh +cftmpr3n5:kat temperature? (Because of this high temperature, the nose of a space vehicle must be made of special materials; indeed, part of it does vaporize, and this is seen as a bright blaze upon reentry.)    K

  The temperature of an ideal gas is increased 1c z6j, k c* -sk;xmkq6xpwfv;from 110$^{\circ} $C to 360$^{\circ} $C while the volume and the number of moles stay constant. By what factor does the pressure change? By what factor does $v_{rms}$ change?$\frac{P_2}{P_1}$ =    $\frac{(v_{rms})_2}{(v_{rms})_1}$ =   

  A house has a volume of -n*wk)na; wgn 770m$^2$ (a) What is the total mass of air inside the house at 20$^{\circ} $C?    kg
(b) If the temperature drops to -10$^{\circ} $C what mass of air enters or leaves the house?    kg

  From the known value of atmospheric pressure at the surface/ 2pedc)trdq 6 of the Earth, estima2t)d/c eq6prdte the total number of air molecules in the Earth’s atmosphere.    $ \times10^{44 }$ molecules

  What is the rms speed of nitrogen nu6/j8plskd (molecules contained in a 7.6$-m^3$ volume at 4.2 atm if the total amount of nitrogen is 1800 mol?    m/s

  A standard cylinder of oxygen used in a hospital has gauge pressure = 2000 ju fuim +r13w;psi (13,800 kPa) and at T = i3mw +r;uufj1 259K How long will the cylinder last if the flow rate, measured at atmospheric pressure, is constant at 2.4 L/min. $\approx$    hour

  An iron cube floats in a bowl of liquid mert b9 u1sx0v* gwq*zgc(cury at 0$^{\circ} $C. (a) If the temperature is raised to 25$^{\circ} $C, will the cube float higher or lower in the mercury? ----待选择----lowerheigher 
(b) By what percent will the fraction of volume submerged change?    %

  The density of gasoly /hdf)vsm;+6a xkl2m ine at 0$^{\circ} $C is 0.68$ \times10^{3 }kg/m^3$ What is the density on a hot day, when the temperature is 38$^{\circ} $C?    kg/$m^3$
What is the percentage change?    %

  If a steel band were kv)0mur 50brhto fit snugly around the Earth’s equator at 25$^{\circ} $C, but then was heated to 45$^{\circ} $C, how high above the Earth would the band be (assume equal everywhere)?    m

  A brass lid screws tightly ontok9.ppix5px m:/*z cq myd6eh+ a glass jar at 20$^{\circ} $C. To help open the jar, it can be placed into a bath of hot water. After this treatment, the temperatures of the lid and the jar are both 60$^{\circ} $C. The inside diameter of the lid is 8.0 cm at 20$^{\circ} $C. Find the size of the gap (difference in radius) that develops by this procedure.    cm

  The first length staf/0nf5bm n u)tndard, adopted in the 18$^{th}$ century, was a platinum bar with two very fine marks separated by what was defined to be exactly 1 m. If this standard bar was to be accurate to within $\pm1.0 \mu m$ how carefully would the trustees have needed to control the temperature? The coefficient of linear expansion for platinum is $ 9\times10^{ -6}C/^{-1}$. $\pm$ =    C$^{\circ} $

  A scuba tank, when fully charged, has a ss v sa9c/a8*mpressure of 195 atm at 20$^{\circ} $C. The volume of the tank is 11.3 L.
(a) What would the volume of the air be at 1.00 atm and at the same temperature?    L
(b) Before entering the water, a person consumes 2.0 L of air in each breath, and breathes 12 times a minute. At this rate, how long would the tank last?    min
(c) At a depth of 20.0 m of sea water and temperature of 10$^{\circ} $C, how long would the same tank last assuming the breathing rate does not change?    min

  The escape speed from the Earth ii j*uoii ( gy3r6coez. f. dhpxw0,85rs $ 1.12\times10^{4 } m/s$ so a gas molecule travelling away from Earth near the outer boundary of the Earth’s atmosphere would, at this speed, be able to escape from the Earth’s gravitational field. At what temperature is the average speed of
(a) oxygen molecules,    $ \times10^{5 }$K
(b) helium atoms equal to $ 1.12\times10^{4 } m/s$    $ \times10^{4}$K
(c) Can you see why our atmosphere contains oxygen but not helium?

  A 1.0-kg trash-can lid is suspended against gravi zgeg )ri16dofctcy /+nf+y- )ty by tennis balls thrown vertically)nteycfd-go 6)+ z/yi1 gr+cf upward at it. How many tennis balls per second must rebound from the lid elastically, assuming they have a mass of 0.060 kg and are thrown at 12m/s   balls/s

  A scuba diver releases a 3.00-cm-diameter (9imw 0 8x kp2o:hbyi;xspherical) bubble of air from a depth of 14.0 m in a lake. Assume the temperature is constant at 298 K, and the air behaves as a perfect gas. How large is the bubble when it reaches the surfa 9xmk:hy ixip0w o8;b2ce?    cm

  Calculate the total water vapor press/u-trj8 dmlf pn9i 7wqkl19p(ure in the air on the following two days: qdt m rn8fw1lp799ip/-j(lku
(a) a hot summer day, with the temperature 30$^{\circ} $C and the relative humidity at 40%;    Pa
(b) a cold winter day, with the temperature 5$^{\circ} $C and the relative humidity at 80%.    Pa

  A sauna has 7$m^3$ of air volume, and the temperature is 90$^{\circ} $C. The air is perfectly dry. How much water (in kg) should be evaporated if we want to increase the relative humidity from 0% to 10%? (See Table 13–3.)    kg

  Estimate the percent difference in the density of iron at STP, 4yz lay63e*m( -p+nnwp+oxgtand when it is a solid de*4l pa( wno t pyn+x-mg6+ze3yep in the Earth where the temperature is 2000$^{\circ} $C and under 5000 atm of pressure. Assume the bulk modulus (90$\times 10^9N/m^2$) and the coefficient of volume expansion do not vary with temperature and are the same as at STP.    %  ----待选择----decreaseincrease 

(a) Use the ideal gas law to show that, gsq2v :jn+i4yyos7kq 5,hu+ g for an ideal gas at constant pressure, the couk q:4 ,syy2g7onvihq+gsj+ 5efficient of volume expansion is equal to $\beta$ = 1/T where T is the temperature in kelvins. Compare to Table 13–1 for gases at T = 293K (b) Show that the bulk modulus (Section 9–5) for an ideal gas held at constant temperature is B = P where P is the pressure.

  In humid climates, peopldflnuwi j3qf z/zp0z/6;:m 9ee constantly dehumidify their cellars to prevent rot and mildew. If the cellar in a house (kep6 /ez:/nj3zmffd 0u9iq;pw lzt at 20$^{\circ} $C) has 95 $m^2$ of floor space and a ceiling height of 2.8 m, what is the mass of water that must be removed from it to drop the humidity from 95% to a more reasonable 30%?    kg